The increasing integration of LSIs has led to finer and finer circuit line widths of semiconductor devices. An approach employed to form desired circuit patterns on semiconductor devices uses a step-and-repeat exposure system to reduce and transfer, onto a wafer, a high-precision master pattern (also called a mask, or a reticle particularly when used in a stepper or scanner) formed on a piece of quartz. The high-precision original pattern is written with an electron beam writing apparatus by use of a so-called electron beam lithography technique.
In drawing with an electron beam, a correction process is needed to change a beam irradiation dose such that dimensions of drawing patterns are kept the same as those of design data. The correction process is performed on factors causing variations in the pattern dimensions, such as the proximity effect, the fogging effect, and the loading effect.
In the lithography technique using an electron beam, a resist pattern is formed, for example, by coating a substrate surface with a resist film, irradiating the resist film with an electronic beam, and by performing a development process. Then, an underlying chromium film (light-shielding film) is subjected to etching with the resist pattern used as a mask.
It is known that a CD (Critical Dimension) of the chromium film is different between when a thickness of the resist film after etching the chromium film is thick and when it is thin (see, e.g., Satoru Nemoto et al., “Etch Characterization of Binary Mask Dependence on Mask Material and Resist Thickness for 22 nm Mask Fabrication”, Proc. of SPIE Vol.7379,737907,2009). In the related-art correction process, therefore, a correlation table between the thickness of the resist film after the etching and a CD distribution of the chromium film is prepared, and a film thickness characteristic of the resist film after the etching is measured. Then, a thickness of the resist film after the etching is calculated from an initial thickness of the resist film and the film thickness characteristic of the resist film after the etching. Then, a CD distribution of the chromium film is estimated from the calculated film thickness and the correlation table. Then, a dimension correction amount for the chromium film at each position on the substrate is determined to prepare a dimension correction map. An irradiation dose of the electron beam at each position on the substrate is calculated on the basis of the dimension correction map, and the electron beam is applied in accordance with the calculated irradiation dose (see, e.g., Japanese Unexamined Patent Application Publication No. 2011-198922).
With further miniaturization of semiconductor elements, it is demanded to more accurately calculate the thickness of the resist film after the etching, to correct the irradiation dose of the electron beam, and to increase drawing accuracy.